Using the Central Limit Theorem, it is found that a sample size of 13 is needed.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X. By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].For this problem, using a calculator:
The mean is [tex]\mu = 37.9[/tex]The standard deviation is [tex]\sigma = 14.07[/tex]The sample size needed is n when [tex]s = 4[/tex], as by the Empirical Rule, 95% of the measures are within 2 standard errors of the mean, hence [tex]2s = 8 \rightarrow s = 4[/tex]
[tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
[tex]4 = \frac{14.07}{\sqrt{n}}[/tex]
[tex]4\sqrt{n} = 14.07[/tex]
[tex]\sqrt{n} = \frac{14.07}{4}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{14.07}{4}\right)^2[/tex]
[tex]n = 12.37[/tex]
Rounding up, a sample size of 13 is needed.
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Each square below represents one whole …. What percent is represented by the shaded area?
Answer:
3/4
Step-by-step explanation:
because there are 4 parts and only three are shaded so 3/4
3/4 or .75 or 75%
Which equation has a solution of r = 1/3
Answer:
Step-by-step explanation:
Answer:
A.
Step-by-step explanation:
A.
2 2/3 + r = 3
r = 3 - 2 2/3
r = 1/3
B.
r - 1 = 2/3
r = 1 2/3
C.
3r = 1/3
r = 1/9
D.
4r = 12
r = 3
Answer: A.
Original price of shorts $53.95 Discount 30% Tax 4.5 percent %
Answer:
$39.50 is the final payment.
Step-by-step explanation:
0.3 x 53.95 = 16.185
53.95 - 16.185
= 37.765
0.045 x 37.765 = 1.699425 + 37.765
= 39.464425 and round
Operations
Five football players ate
15/17
of a lasagna. The 5 players ate equal
amounts. How much of the lasagna did each player eat?
Answer:
3
Step-by-step explanation: because 15 divided by 5 equals 3
Identify the given quadrilateral
Can anyone tell me if these are correct?
Which equation has the solution x = 3?
Select each correct answer.
2x + 4 = 10
9−3x=0
3x + 1 = 9
9x−1=4
x3+5=6
5x−7=1 giving 50 pointss so hurry
Answer:
A and B
Step-by-step explanation:
A: 2x3=6 6+4=10 so correct
B: 9-9=0 so correct
Answer:
2x+4=10
Step-by-step explanation:
2x=10-4=
2x=6
x=6÷2=
3
Help please! Mathematics as a teen isn’t my strong suit
Also, number 15) has4 columns and 6 rows
Answer:
ang masasabi ko lang thans sa points
Step-by-step explanation:
salamat sa pointsmore points to come50 points ulit haHi! ❤️ , im looking for some (accurate) help here.
ill give brainliest if able to.
Answer:
A
Step-by-step explanation:
70000 is 100 times greater than 700
The following triangles are similar triangles with some dimensions specified. Find the measures of the other sides.
Answer:
116°
Step-by-step explanation:
(Angle sum property of a triangle = 180°)
angle A + angle C + angle ABC = 180°
66° + 50° + angle BAC = 180°
116° + angle ABC = 180°
angle ABC = 180° - 116°
angle ABC = 64°
angle ABD + angle ABC = 180°
angle ABD + 64° = 180°
angle ABD = 180° - 64°
angle ABD = 116°
So, the measure of the unknown angle is 116°
the independent and dependent variables.
1) You are taking a road trip in a car and want to know how far you've traveled (read the odometer) at various times
during your trip.
A) does not describe a function
B) Independent variable, distance traveled; dependent variable, time
C) Independent variable, time; dependent variable, distance traveled
actont Writon statement that describes how one
Answer:
C) Independent variable, time; dependent variable, distance traveled
Explanation:
An independent variable (also known as the manipulated variable) is the thing you change on purpose. A dependent variable (also known as responding variable) is what you measure on different kinds of trials. You are measuring how far you've gone. You will measure this at various times (you change this).
Correct answer is C : Independent variable, time; dependent variable, distance traveled actont Writon statement that describes how one.
What is Independent variable?The independent variable exists as the variable being regulated in the problem, and the dependent variable exists as the variable that varies because of this control.
It exists a variable that stands alone and isn't altered by the other variables you exist trying to measure.
An independent variable (also known as the manipulated variable) is the thing you change on purpose. A dependent variable (also known as responding variable) is what you measure on different kinds of trials. You are measuring how far you've gone. You will measure this at various times (you change this)To learn more about Independent variable refer to:
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Solve the inequality.
2(x+4) < 2 - x
Answer:
x < -2
Step-by-step explanation:
2(x+4)<2-x
2x+8<2-x
+x +x
3x+8<2
-8 -8
3x<-6
x<-2 Divide both sides by 3
Hope this helps!
Answer:
2x+8<2-x
8-2<-x-2x
-3x>6
x>6/3
x<2
Step-by-step explanation:
I think it's smtg like this
Combining like terms. Solve for b.
15b + 10b = 50
Answer:
b=2
Step-by-step explanation:
15b+10b=50
25b=50
b=2
Answer:
B is 2 because 10x2=20 and 15x2=30
add those 2 up and get 50
Step-by-step explanation:
Give brainly pls(the crown)
A candle factory makes colored candles to sell in packages. Which of the following situations best represents a proportional relationship?
Answer:
D Each package has 8 yellow candle chips. A total of 18 packages will have 144 yellow candle chips.
Step-by-step explanation:
8/1 is proportional to 144/18
In option C and D the number of object increases other object also increases. Therefore, options C and D are the correct answers.
Given that, a candle factory makes colored candles to sell in packages.
What is a proportional relationship?Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is known as the "constant of proportionality".
A) Does not a represents a proportional relationship
B) Does not a represents a proportional relationship
C) The cost of one package is $1.98 and the cost of 10 packages is $16.99.
Here, the number of packages increases, the cost also increases. So, it is direct proportion.
D) In one package there are 8 yellow candle chips and 18 packages will have 144 yellow candle chips.
Here, the number of packages increases, the number of chips also increases. So, it is direct proportion.
In option C and D the number of object increases other object also increases. Therefore, options C and D are the correct answers.
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rebecca has 12 photos she wants to hang side by side on her wall.
A. if she only wants to display 8 of the photos, in how many ways can she choose 8 photos she wishes to eventually display?
B. in how many ways can she arrange all 12 photos?
C. if rebecca wants to have the 10 out of 12 photos in specific places, how many ways could she order the 12 photos?
We want to find different ways of selecting and ordering elements. The answers are:
A) C = 395
B) combinations = 479,001,600
C) combinations = 239,500,800
First, we know that Rebecca has 12 photos.
A) She wants to choose 8 of these 12 photos, we want to see in how many ways she can choose these 8 photos.
Remember that for a set of N elements, the number of different combinations of K elements (such that K is smaller than N) is given by:
[tex]C(N, K) = \frac{N!}{(N - K)!*K!}[/tex]
Here we have N = 12 and K = 8, then:
[tex]C(12, 8) = \frac{12!}{(12 - 8)!*8!} = \frac{12!}{4!*8!} = \frac{12*11*10*9}{4*3*2*1} = 495[/tex]
So there are 495 different ways of choosing 8 photos out of the 12.
B) Now we want to see in how many ways she can arrange all 12 photos.
The first photo can be any one of the 12, so there we have 12 options.The second photo can be any one of the remaining 11 (so we have 11 options).The third photo can be any one of the remaining 10, and so on.The total number of combinations is just the product between the numbers of options, we got:
[tex]combinations = 12*11*10*9*8*7*6*5*4*3*2*1 = 479,001,600[/tex]
C) Now we must combine the two things we did before, first, we select 10 out of the 12 photos, and then we want to find in how many ways we can arrange these 10 photos.
[tex]C(12, 10) = \frac{12!}{(12 - 10)°*10°} = \frac{12*11}{2} = 66[/tex]
And we multiply this by the total number of arrangements of these 10 photos, that is just given by 10!, so we get:
[tex]c = 66*10! = 66*(10*9*8*7*6*5*4*3*2*1) = 239,500,800[/tex]
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which matrix multiplication is defined?
Please help I do not really know what I’m doing if you could give an example of that would be good too but if not that’s OK
Answer:
the dot would be shaded in and from -6 go to the left
Step-by-step explanation:
5 lb 6 oz = __________ oz
Explain yourself
Answer:
86 oz
Step-by-step explanation:
1 lb = 16 oz
5 lb * 16 oz = 80 oz
80 oz + 6 oz = 86 oz
An investor has an account with stock from two different companies. Last year, his
stock in Company A was worth $2000 and his stock in Company B was worth $4240.
The stock in Company A has increased 1% since last year and the stock in Company B
has increased 5%. What was the total percentage increase in the investor's stock
account? Round your answer to the nearest tenth (if necessary).
Answer:
Submit Answer
acer
Answer:
Total percent: 3.7%
Step-by-step explanation:
(2000 x 0.01) + (4240 x 0.05) = $232
X/100 = 232/6240
= 23200/6240 = 3.7%
Willie stands on one side of a cart and pushes with a force of 100 Newtons. Jenny stands on the others side of a filing cabinet and pushes with a force of 100 Newtons. If Willie wants to help Jenny demonstrate balanced forces, what does Willie need to do?
Willie needs to keep same force acting by him on the cart inorder to balance the force.
Let's check how?
F_1=100NF_2=-100N[tex]\\ \sf\longmapsto F_{net}=100-100=0N[/tex]
.Hence verified
Which point is a solution to the system?
Answer:
d
Step-by-step explanation:
A model rocket is launched with an initial upward velocity of 125/fts. The rocket's height h (in feet) after t seconds is given by the following.
h=125t- -16t^2
Answer:
H = V0 t + 1/2 g t^2 is the equation in question with V0 and g in different directions, they have different signs
0.5 ÷ 10.2 If you solve this, can you show the steps of this equation?
Answer:
0.5/ 10.2
Well its basically
Well first you gotta make sure the 10.2 is a whole number in order to divide
so we can multiply by 10
that turns it into 102
Now what we do do 10.2 we do to 0.5 to make it equal which makes0.5*10=5
Now its easier so its 5/102
Now we just divide normally
*assuming its rounded to the nearest hundredths
0.05
what is the value of 2
Step-by-step explanation:
???
one more than 1, one less than 3
Answer:
the value of 2 is 1+1=2
Step-by-step explanation:
gamsahamnida have a great day ahead
12 x 12 x 12 = 4 x # x 4 what number must replace the '#' symbol
Answer:
I'm pretty sure it's 108.
Step-by-step explanation:
12 x 12 x 12 = 1,728
4 x 4 = 16
1,728 ÷ 16 = 108
Three friends do
Word together for 5 days. The first friend does it alone for 15days. The second friend does it alone for 12 days.
many days does the third do it alone for?
Answer:
I think 9 days
Pls mark as brainliest answer if it helps you
in one month we have 31 days so
31-15-12=4hope it helpsAre the triangles congruent! (Help)
What is the slope of the line that
passes through the points (-1, 3)
and (2, 10)?
Answer:
D [tex]\frac{7}{3}[/tex]
Step-by-step explanation:
For find the slope of whatever line we use the next formula:
[tex]m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
So in our occasion we have:
[tex]y_2 = 10 \quad \text{and} \quad y_1 = 3\\x_2 = 2 \quad \text{and} \quad x_1 = -1[/tex]
Replacing in the equation:
[tex]\frac{10 - 3}{2 - (-1)} = \frac{7}{3}[/tex]
So the answer is [tex]\frac{7}{3}[/tex]
Evaluate the expression -2
Answer: 2x for x=3: 2(3) = 6.
Step-by-step explanation:
The table shows that the ratio of boys to girls at Midtown Middle School is 3 to 4. Which classes have an equivalent ratio of boys to girls? Check all that apply. A math class with 12 boys and 16 girls.
An English class with 14 boys and 14 girls.
A science class with 15 boys and 20 girls.
A Spanish class with 20 boys and 15 girls.
A band class with 75 boys and 100 girls.
Answer:
Step-by-step explanation:
A math class with 12 boys and 16 girls, A science class with 15 boys and 20 girls and A band class with 75 boys and 100 girls have an equivalent ratio of 3 : 4.
What is Ratio?Ratio is a concept in mathematics used to compare two things.
It is denoted by a : b.
A ratio can be represented as fractions also like a/b.
In the question, it is given that the ratio of boys to girls is 3 to 4.
A math class with 12 boys and 16 girls = 12/16 = 3/4An English class with 14 boys and 14 girls = 14/14 = 1A science class with 15 boys and 20 girls = 15/20 = 3/4A Spanish class with 20 boys and 15 girls = 20/15 = 4/3A band class with 75 boys and 100 girls = 75/100 = 3/4Hence A math class with 12 boys and 16 girls, A science class with 15 boys and 20 girls and A band class with 75 boys and 100 girls have an equivalent ratio of 3 : 4.
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If a 32 ft. tall tree casts an 8 ft. shadow , how long of a shadow dc 6 ft. tall man have?
Answer:
1.5ft
Step-by-step explanation:
32/8=4
32/4=8
6/4=1.5